(EDIT I know this is long: tl;dr
I live in northern Cincinnati, so about equidistant between CVG and DAY. I came up with the following

JFK-MAD-MXP-LHR-ORD-LAX-SYD-DFW-DAY-DFW-HNL-ORD-CVG-MIA-CUN-ORD 39336 miles - any issues with that?)

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So I had heard about these OneWorld explorer awards but came across them again recently with a post about the idea of using one award to plan multiple smaller vacations on the "same" award. I spent a bit of time putting together a possible routing and wanted to run it by you guys to see if there are any thoughts.

I live in northern Cincinnati, so about equidistant between CVG and DAY. I came up with the following

JFK-MAD-MXP-LHR-ORD-LAX-SYD-DFW-DAY-DFW-HNL-ORD-CVG-MIA-CUN-ORD 39336 miles

(details)

CVG-JFK Thursday 4/3 12:30pm - Thursday 4/3 14:35 - positioning, book with Avios

JFK-MAD-MXP-LHR-ORD
1. JFK-MAD Iberia 6252, Thursday 4/3 20:45 - Friday 4/4 10:00
2. MAD-MXP Iberia 3254, Friday 4/4 15:50 - Friday 4/4 18:10
3. MXP-LHR BA 567, Saturday 4/5 19:00 - Saturday 4/5 19:55
4. LHR-ORD BA 1542, Sunday 4/6 10:15 - Sunday 4/6 13:00

ORD-CVG American 2954 Sunday 4/6 15:00 - Sunday 4/6 17:05 - positioning, book with Avios
DAY-ORD American 3342 Tuesday 9/9 16:40 - Tuesday 9/9 16:55 - positioning, book with Avios

ORD-LAX-SYD-DFW-DAY
5. ORD-LAX American 1398 Tuesday 9/9 19:10 - Tuesday 21:45
6. LAX-SYD Qantas 108 Tuesday 9/9 23:50 - Thursday 7:40
7. SYD-DFW Qantas 7, Saturday 9/13 13:25 - Sunday 9/14 13:45
8. DFW-DAY American 1264, Sunday 9/14 18:54 - Sunday 9/14 22:04

DAY-DFW-HNL-ORD-CVG
9. DAY-DFW American 1217 Wednesday 12/18 6:55 - Wednesday 12/18 8:55
10. DFW-HNL American 5 Wednesday 12/18 13:05 - Thursday 12/19 17:45
11. HNL-ORD American 72 Saturday 12/21 17:00 - Sunday 12/22 5:25
12. ORD-CVG American 5364 Sunday 12/22 11:25 - Sunday 12/22 13:35

CVG-MIA-CUN-ORD-XXX
13. CVG-MIA American 3355 Thursday 2/6 7:30 - Thursday 2/6 10:15
14. MIA-CUN American 2422 Thursday 2/6 14:15 - Thursday 2/6 15:10
15. CUN-ORD American 184 Sunday 2/9 8:10 - Sunday 2/9 11:50
16. ORD-XXX By my understanding since I have a stopover in ORD I can't end there, so my thought was to schedule my 16th segment from ORD to wherever and then "forget" to board, and instead board my positioning flight back to CVG

ORD-CVG American 3062 Sunday 2/9 14:30 - Sunday 2/9 16:35 - positioning, book with Avios

So, if I did things right, that's 4 vacations to Europe, Sydney, Hawaii and Cancun for 180,000 AAdvantage miles + 18,000 Avios (economy)

In looking at the rules in the first post:
16 segments
1 open jaw (from beginning the award in JFK to ending in ORD)
39,336 miles which is actually leaving some on the table
Connections: JFK (start), LAX, DFW (twice), ORD (twice), MIA
Stopovers: MAD, MXP, LHR, ORD, SYD, DAY, HNL, CVG, CUN
At least 2 partner airlines: Iberia, BA, Qantas
Travel within 1 year: check

This is still in the hypothetical stages, and if I had the miles in hand yet, there are a few optimizations I might make, such as trying to avoid British Airways for the fuel surcharges, or arranging things so my 15th segment is in CVG allowing me to again "forget" to board my last segment and save on the last positioning flight back home.

Also, I have not yet accounted for award availability, or maximizing the "best" business class products, and the dates are a bit off because I used a mixture of 2013 and 2014 dates

But does this look like a basic framework of something that might work?